Modern Control Engineering

Section 6–6 / Lead Compensation 319

MATLAB Program 6–9, where num1 and den1 denote the numerator and denominator of the

system designed by Method 1 and num2 and den2 denote that designed by Method 2. Also, num

and den are used for the original uncompensated system. The resulting unit-step response curves

are shown in Figure 6–45. The MATLAB program to obtain the unit-ramp response curves of the

MATLAB Program 6–9

% Unit-Step Response of Compensated and Uncompensated Systems

num1 = [12.287 23.876];

den1 = [1 5.646 16.933 23.876];

num2 = [9];

den2 = [1 3 9];

num = [10];

den = [1 1 10];

t = 0:0.05:5;

c1 = step(num1,den1,t);

c2 = step(num2,den2,t);

c = step(num,den,t);

plot(t,c1,'-',t,c2,'.',t,c,'x')

grid

title('Unit-Step Responses of Compensated Systems and Uncompensated System')

xlabel('t Sec')

ylabel('Outputs c1, c2, and c')

text(1.51,1.48,'Compensated System (Method 1)')

text(0.9,0.48,'Compensated System (Method 2)')

text(2.51,0.67,'Uncompensated System')

Outputs

c1,

c2, and

c

0.4

0.8

1.8

0

0 0.5 1 1.5 2 2.5

t Sec

3 3.5 4 4.5 5

1.2

0.6

1

0.2

1.4

1.6

Unit-Step Responses of Compensated Systems and Uncompensated System

Compensated System (Method 1)

Compensated System (Method 2)

Uncompensated System

Figure 6–45
Unit-step response
curves of designed
systems and original
uncompensated
system.